Algebraic approach to equivariance of solutions for an iterative equation

• Autores: W. Zhang, Bing Xu
• Localización: Publicationes Mathematicae Debrecen, ISSN 0033-3883, Tomus 72, Fasc. 1-2, 2008, págs. 189-198
• Idioma: inglés
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• Resumen

  • Describing the symmetry of a mapping by equivariance with respect to a lin- ear transformation group, the reference [Proc. Roy. Soc. Edinburgh A130 (2000), 1153{1163] gave the existence of equivariant solutions of the polynomial-like iterative equation under the action of topologically ¯nitely generated subgroups of GL(R) on R and the orthogonal group O(N) on RN (N ¸ 2). In this paper, based on the algebraic structure of closed subgroups of GL(R), we prove the equivariance of solutions on R with respect to closed subgroups of GL(R) and extend the result of O(N)-equivariance of solutions to the group O(N) £ hcINi on RN.